The company reported Q1 net income of $52 million, besting larger rivals Royal Caribbean Cruises Ltd. (RCCL), which reported net income of $26.5 million, and Carnival Corp., which reported a $15 million loss.

When asked in a conference call by one Wall Street analyst when Norwegian would achieve the steady price advantage enjoyed by Disney Cruise Line, Sheehan argued he's mostly there.

"We have stood out significantly from the industry," Sheehan said. In comparing first-quarter prices, "we are probably 800 or 900 basis points different from our competitors."

Higher prices are a key metric for travel agents because of their correlation with higher commissions.

"We have stepped up from being a distant third to being best in class," Sheehan argued.

Undoubtedly a big chunk of the improvement came from including the premium fares commanded by the Norwegian Breakaway and Getaway in this year's quarter. The Breakaway began sailing in May 2013, while the Getaway started the first week in February.

Sheehan confirmed that those ships, as well as the Norwegian Epic, continue to enjoy double-digit price advantages over the rest of Norwegian's 13-ship fleet.

In last year's first quarter, Norwegian reported a $97.5 million loss. After adjusting for various special items, Norwegian said its first-quarter profits were $49.6 million this year and $12.9 million last year.

Revenue rose 26%, to $664 million.

Assia Georgieva, an analyst with Infinity Research, said she was impressed with the rise in ticket yields. "I think that was quite spectacular," she said. By comparison, ticket revenues at RCCL declined 3% during the quarter.

But other analysts looking to the future said they were concerned about the duration of the price swoon in the Caribbean and the scheduled arrival of the Norwegian Escape in Miami in 2015.

"The Caribbean is still a bit behind where we want it to be," Sheehan acknowledged. But he said the excess capacity would eventually clear, and pointed to the departure of the MSC Divina for Europe in the summer of 2015 as one sign it is happening.

He said that as the 4,200-passenger Escape arrives in Miami, the 4,100-passenger Epic would shift to Europe full-time, so the capacity increase it represents will be minimal.

Sheehan said that in addition to being big revenue producers, the new ships are far more efficient. "I hope everyone understands that," he said. If promotions abate in the Caribbean, a more affluent customer should drive onboard spending higher, he added.

Next year, Norwegian will have 45% of its capacity in the Caribbean and 21% in Europe, with the balance in Alaska, Hawaii and elsewhere.

Sheehan noted the past 10 weeks have seen "significantly positive bookings. You sense we're beginning to feel that things would start to improve."

Asked about developing Norwegian's presence in the Asia-Pacific region, Sheehan said, "It's been on our radar."

"I would suspect over the next year or so you will see some action from us," he said.